diff --git a/include/mlir/Dialect/Linalg/ComprehensiveBufferize/BufferizableOpInterface.h b/include/mlir/Dialect/Linalg/ComprehensiveBufferize/BufferizableOpInterface.h
index e03aaea..52befbd 100644
--- a/include/mlir/Dialect/Linalg/ComprehensiveBufferize/BufferizableOpInterface.h
+++ b/include/mlir/Dialect/Linalg/ComprehensiveBufferize/BufferizableOpInterface.h
@@ -327,10 +327,9 @@
   virtual ~PostAnalysisStep() {}
 
   /// Run the post analysis step. This function may modify the IR, but must keep
-  /// `aliasInfo` consistent. Newly created operations and operations that
-  /// should be re-analyzed must be stored in `newOps`.
-  virtual LogicalResult run(FuncOp funcOp, BufferizationAliasInfo &aliasInfo,
-                            DominanceInfo &domInfo,
+  /// `aliasInfo` (inside `state`) consistent. Newly created operations and
+  /// operations that should be re-analyzed must be stored in `newOps`.
+  virtual LogicalResult run(FuncOp funcOp, BufferizationState &state,
                             SmallVector<Operation *> &newOps) = 0;
 };
 
diff --git a/include/mlir/Dialect/Linalg/ComprehensiveBufferize/LinalgInterfaceImpl.h b/include/mlir/Dialect/Linalg/ComprehensiveBufferize/LinalgInterfaceImpl.h
index d5ee20b..1858787 100644
--- a/include/mlir/Dialect/Linalg/ComprehensiveBufferize/LinalgInterfaceImpl.h
+++ b/include/mlir/Dialect/Linalg/ComprehensiveBufferize/LinalgInterfaceImpl.h
@@ -34,7 +34,7 @@
   /// * The result of `rewriteFunc` must usually be analyzed for inplacability.
   ///   This analysis can be skipped with `skipAnalysis`.
   LogicalResult eliminateInitTensors(
-      FuncOp funcOp, BufferizationAliasInfo &aliasInfo, DominanceInfo &domInfo,
+      FuncOp funcOp, BufferizationState &state,
       std::function<bool(OpOperand &)> anchorMatchFunc,
       std::function<Value(OpBuilder &, Location, OpOperand &)> rewriteFunc,
       SmallVector<Operation *> &newOps);
@@ -45,8 +45,7 @@
 /// (and some other conditions are met).
 struct InsertSliceAnchoredInitTensorEliminationStep
     : public InitTensorEliminationStep {
-  LogicalResult run(FuncOp funcOp, BufferizationAliasInfo &aliasInfo,
-                    DominanceInfo &domInfo,
+  LogicalResult run(FuncOp funcOp, BufferizationState &state,
                     SmallVector<Operation *> &newOps) override;
 };
 
diff --git a/lib/Dialect/Linalg/ComprehensiveBufferize/ComprehensiveBufferize.cpp b/lib/Dialect/Linalg/ComprehensiveBufferize/ComprehensiveBufferize.cpp
index 53eaab5..eb37a54 100644
--- a/lib/Dialect/Linalg/ComprehensiveBufferize/ComprehensiveBufferize.cpp
+++ b/lib/Dialect/Linalg/ComprehensiveBufferize/ComprehensiveBufferize.cpp
@@ -728,7 +728,7 @@
   for (const std::unique_ptr<PostAnalysisStep> &step :
        options.postAnalysisSteps) {
     SmallVector<Operation *> newOps;
-    if (failed(step->run(funcOp, aliasInfo, domInfo, newOps)))
+    if (failed(step->run(funcOp, state, newOps)))
       return failure();
     // Analyze ops that were created by the PostAnalysisStep.
     if (failed(inPlaceAnalysis(newOps, aliasInfo, domInfo)))
diff --git a/lib/Dialect/Linalg/ComprehensiveBufferize/LinalgInterfaceImpl.cpp b/lib/Dialect/Linalg/ComprehensiveBufferize/LinalgInterfaceImpl.cpp
index 7bea450..b4a439e 100644
--- a/lib/Dialect/Linalg/ComprehensiveBufferize/LinalgInterfaceImpl.cpp
+++ b/lib/Dialect/Linalg/ComprehensiveBufferize/LinalgInterfaceImpl.cpp
@@ -407,12 +407,12 @@
 /// OpOperand, that eventually ends at a single InitTensorOp.
 LogicalResult mlir::linalg::comprehensive_bufferize::linalg_ext::
     InitTensorEliminationStep::eliminateInitTensors(
-        FuncOp funcOp, BufferizationAliasInfo &aliasInfo,
-        DominanceInfo &domInfo,
+        FuncOp funcOp, BufferizationState &state,
         std::function<bool(OpOperand &)> anchorMatchFunc,
         std::function<Value(OpBuilder &, Location, OpOperand &)> rewriteFunc,
         SmallVector<Operation *> &newOps) {
   OpBuilder b(funcOp->getContext());
+  BufferizationAliasInfo &aliasInfo = state.aliasInfo;
 
   WalkResult status = funcOp->walk([&](Operation *op) {
     for (OpOperand &operand : op->getOpOperands()) {
@@ -501,17 +501,17 @@
 /// out-of-place due to RaW conflicts.
 LogicalResult mlir::linalg::comprehensive_bufferize::linalg_ext::
     InsertSliceAnchoredInitTensorEliminationStep::run(
-        FuncOp funcOp, BufferizationAliasInfo &aliasInfo,
-        DominanceInfo &domInfo, SmallVector<Operation *> &newOps) {
+        FuncOp funcOp, BufferizationState &state,
+        SmallVector<Operation *> &newOps) {
   return eliminateInitTensors(
-      funcOp, aliasInfo, domInfo,
+      funcOp, state,
       [&](OpOperand &operand) {
         auto insertSliceOp =
             dyn_cast<tensor::InsertSliceOp>(operand.getOwner());
         if (!insertSliceOp)
           return false;
         // Only inplace bufferized InsertSliceOps are eligible.
-        if (!aliasInfo.isInPlace(insertSliceOp->getOpResult(0)))
+        if (!state.aliasInfo.isInPlace(insertSliceOp->getOpResult(0)))
           return false;
         return &operand == &insertSliceOp->getOpOperand(0) /*source*/;
       },